NUT ENGINEERING TOOLS

Sector / Segment Solver

See It. Solve It. Understand It.

Enter a valid combination of circle measurements. Nut calculates sector area, segment area, arc length, chord length, sagitta, and related geometry.

Live Geometry

Diagram updates when the sector and segment geometry is solved.

Enter What You Know

Enter a valid combination of measurements. Leave unknown values blank.

Radius Diameter Central Angle

Arc Length Chord Length Sagitta / Arc Height Sector Area Segment Area

Calculated Results

Complete sector and segment geometry from the measurements you entered.

Radius —

Diameter —

Central Angle —

Arc Length —

Chord Length —

Sagitta —

Sector Area —

Segment Area —

Nut shows the actual equations and values used to solve the sector and segment.

Enter known measurements and solve the geometry to see the calculation steps.

Sector and segment areas are determined from the radius and central angle.

A_sector = ½r²θ

A sector is the wedge-shaped region bounded by two radii and the arc between them. The angle θ is expressed in radians.

A_triangle = ½r² sin(θ)

The two radii and chord form a triangle inside the sector.

A_segment = ½r²(θ − sin θ)

A circular segment is the region between the chord and its arc.

s = rθ

Arc length equals radius multiplied by the central angle in radians.

c = 2r sin(θ ÷ 2)

The chord is the straight line connecting the endpoints of the arc.

h = r − r cos(θ ÷ 2)

Sagitta is the maximum perpendicular rise from the chord to the arc.

Nut Industries V2 — Development Preview